Experimental investigation of new materials, medicines or other species requires spectroscopic characterization of the prepared samples to reveal their structure. Vibrational spectroscopy is a very important class of techniques including, amongst others, infrared (IR) spectroscopy, Raman spectroscopy and inelastic neutron scattering. The result of these measurements is an absorption or transmission rate of radiation, as a function of the wavenumber. In Figure 1 an IR-spectrum of ethanol is displayed.

Figure 1. IR transmission spectroscopy of ethanol.

These spectra can be used as a fingerprint of a sample containing one or more compounds of interest. Every peak can, in principle, be associated with a vibrational eigenmode at the atomic scale. Experimentally, the assignment of peaks to groups of atoms (e.g. CH3) is done empirically and allows one to unravel the composition of the sample. Obviously this empirical approach is only applicable to relatively simple molecular structures.

Using Molecular Dynamics (MD) simulations, the vibrational spectra can also be determined by exclusively using theoretical tools. In an MD simulation, Newton’s equations of motion are integrated for atomic particles, resulting in a trajectory of every particle as a function of time for a given temperature. These trajectories can be regarded as time-signals which are easier to interpret using frequencies. For example, a Fourier transform of atomic velocities results in an INS spectrum and other types of vibrational spectra can be derived by computing the Fourier transform of other quantities. As an alternative for MD, the harmonic oscillator approach can be used to compute the vibrational eigenmodes. In realistic systems however, the spectrum is influenced by anharmonic effects which can only be fully accounted for by using MD simulations. Since the MD simulations contain all information of the atomic motions, it is – in principle – possible to assign each peak to a vibrational mode. This information is very valuable for experimental characterization of studied samples. The Center for Molecular Modelling (CMM) has made significant progress, however, a foolproof protocol for the accurate analysis of the spectra does not yet exist. This thesis intends to fill this gap. Method development in combination with programming and simulations will thus be essential during this thesis.

Goal The goal of this thesis is the development of a method to decompose the simulated spectrum – based on MD simulations – into its individual peaks, each to be identified by a clear eigenmode. Additional challenges include the anharmonic effects, which troubles the unique definition of these eigenmodes. The decomposition is schematically represented in Figure 2. This development will allow improved interpretation of vibrational spectra and material characterization.

Figure 2. Decomposition of a spectrum.

This thesis contains both theoretical development (modeling) and implementation of these methods (programming). It will require several aspects of signal analysis and a good physical insight in Newtonian mechanics. According to the interest of the student, the focus can be very fundamental (to develop a model that is fully automated), or a more empirical approach can be used.